657972 has 54 divisors (see below), whose sum is σ = 1939938. Its totient is φ = 187488.

The previous prime is 657959. The next prime is 657973. The reversal of 657972 is 279756.

It can be written as a sum of positive squares in only one way, i.e., 571536 + 86436 = 756^2 + 294^2 .

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 657972.

It is not an unprimeable number, because it can be changed into a prime (657973) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 1578 + ... + 1950.

2⁶⁵⁷⁹⁷² is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 657972, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (969969).

657972 is an abundant number, since it is smaller than the sum of its proper divisors (1281966).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

657972 is a wasteful number, since it uses less digits than its factorization.

657972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 397 (or 385 counting only the distinct ones).

The product of its digits is 26460, while the sum is 36.

The square root of 657972 is about 811.1547324648. The cubic root of 657972 is about 86.9766088522.

The spelling of 657972 in words is "six hundred fifty-seven thousand, nine hundred seventy-two".